Research projects

• ECHO: Education, Community, and Health Observations

  • Information and spatial segregation

• Quantifying state violence

  • Prisons, a history of the U.S.

  • Policing, power and punishment.

  • The divided states of america: Politics and the development of an empire

• Statistics and data science education

  • Teaching statistical learning and mathematical modeling

  • Computation and adult learning

• Maintaining complex theory in quantification

  • Theories and conceptions of race and racism

Research projects

• ECHO: Education, Community, and Health Observations

  • Information and spatial segregation

• Quantifying state violence

  • Prisons, a history of the U.S.

  • Policing, power and punishment.

  • The divided states of america: Politics and the development of an empire

• Statistics and data science education

  • Teaching statistical learning and mathematical modeling

  • Computation and adult learning

• Maintaining complex theory in quantification

  • Theories and conceptions of race and racism

Information and spatial segregation

How have histories of racial segregation informed education, community, and health outcomes?

Chodrow (2017), examines residential segregation using a taxonomy of smoothing-based segregation metrics, we consider key historical components and markers in the development of a history of “dividing walls”.

• Historical legacies of injustice. “The 1968 [Fair Cities] Act expanded on previous acts and prohibited discrimination concerning the sale, rental, and financing of housing based on race, religion, national origin, sex, (and as amended) handicap and family status.” (US Housing and Urban Development, n.d)

• Traditional modeling approaches. What has been done more recently and historically?

• Modern computational tools. What new (grounded) theoretical insights can be identified?

Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.

Geographic area with neighborhood units

Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.

Geographic area with wall dividing neighborhood units

Is there a dividing wall for an island with coastal towns?

Island with coastal towns

Is there a dividing wall for an island with coastal towns?

Minimal configuration

Theorem 2. Alternating configurations of towns do not have a dividing wall, whereas non-alternating configurations of towns do have a dividing wall.

Alternating configuration (left) and non-alternating configuration (right).

Algebraic approach

We then develop a algebraic modeling approach using methods from mathematical sociology.

Segregation indices

• Dissimilarity index: Measures the proportion of one group’s population that would need to move to achieve an even distribution across all areas. It ranges from 0 to 1, with higher values indicating greater segregation.

• Isolation index: Measures the extent to which members of a particular group are surrounded by others from the same group. It represents the percentage of people from a specific group who would need to change neighborhoods to achieve an even distribution. Higher values indicate higher isolation and segregation.

Algebraic approach

We then develop a algebraic modeling approach using methods from mathematical sociology.

Segregation indices

• Exposure index: Measures the extent to which members of one group are exposed to members of another group. It quantifies the likelihood that a randomly selected individual from one group will encounter individuals from another group. Higher values indicate higher exposure and lower segregation.

• Concentration index: Measures the extent to which a particular group is concentrated in specific areas or neighborhoods. It reflects the degree of clustering or dispersion of the group’s population across geographic units.

• Gini index: Measure of income inequality, but it can also be adapted to measure residential segregation. It provides a summary measure of the overall distribution of different groups across neighborhoods.

## Racial isolation from an algebraic geometry approach

Horizontal configuration.

## Racial isolation from an algebraic geometry approach

Vertical configuration.

Index of Dissimilarity

\[ D = \dfrac{1}{2} \sum_\limits{i=1}^n \bigg| \text{Proportion of Black units} - \text{Proportion of non-Black units} \bigg| \]

• \(n\) is the number of neighborhoods in a geographic region,

• \(b_i\) is the number of Black household units in neighborhood \(i\),

• \(B\) is the total number of Black household units in the geographic region,

• \(w_i\) is the number of non-Black household units in neighborhood \(i\),

• \(W\) is the total number of non-Black household units in the geographic region.

Index of Dissimilarity

\[ D = \dfrac{1}{2} \sum_\limits{i=1}^n \bigg| \dfrac{b_i}{B} - \dfrac{w_i}{W} \bigg| \]

- $n$ is the number of neighborhoods in a geographic region, 

• \(b_i\) is the number of Black household units in neighborhood \(i\),

• \(B\) is the total number of Black household units in the geographic region,

• \(w_i\) is the number of non-Black household units in neighborhood \(i\),

• \(W\) is the total number of non-Black household units in the geographic region.

Computational approach

Teaching computational methods and open source tools makes for efficient and accurate learning. In about 5 lines of code, there is an immediate intersection of theory and computation.

Here we use the tidycensus() package to gather various metrics.

Prisons

To support our framing of contemporary data, we take on an historical view.

Racism vs. Anti-Blackness

In a 2020 NY Times article, kihana miraya ross chronicles the realities of anti-Blackness. ross (2020) deals with the related but differing functions of racism and anti-Blackness.

Project background: Information and spatial segregation

Information and theory

How have histories of segregation informed education, health, and political outcomes?

• Racial segregation

Photo: Universal History Archive–Universal Images Group

How have histories of segregation informed education, health, and political outcomes?

• Racial segregation

• Economic segregation

Photo: Brookings Institution

How have histories of segregation informed education, health, and political outcomes?

• Racial segregation

• Economic segregation

• Dynamic features of isolation (e.g., measures of segregation)

Photo: DC Policy Center

Mapping Single Dimensions

Theoretical framework: A Patchwork Nation

Theoretical framework: A Patchwork Nation

Analytic framework: Community Resilience Estimates

• The Census Community Resilience Estimates (CRE) data sets were developed to assess the social vulnerability and resilience of neighborhoods in response to disasters or shocks.

  – Households with an income-to-poverty ratio less than 130%

  – Less than one individual living in the household is aged 18–64

  – Household crowding, defined as more than 0.75 persons per room

  – Households with limited education

  – No one in the household is employed full-time year-round

  – Individual with a disability posing a constraint to significant life activity

  – Individual with no health insurance

  – Individual aged 65 or older

  – Households without a vehicle

  – Households without broadband internet access

Analytic framework: Community Resilience Estimates

• CRE estimates are a measure of the capacity of individuals and households within a community to absorb, endure, and recover from external stresses.

• The CRE data combine American Community Survey (ACS) and the Population Estimates Program (PEP) data to identify social and economic vulnerabilities by geography.

• There is a nice CRE Interactive Tool that allows for a quick overview of local contexts.

cre_correlates_dc <- get_acs(
  geography = "tract", state = "DC", year = 2023, survey = "acs5",
  variables = c(
    median_income = "B19013_001",       # Median household income in the past 12 months
    poverty_rate = "B17001_002",        # Number of people below poverty level
    unemployment_rate = "B23025_005",   # Number of civilians (16 years and over) unemployed
    no_health_insurance = "B27010_033", # Number of people with no health insurance coverage
    educ_less_than_hs = "B15003_002",   # Population 25 years and over with less than 9th grade education
    median_age = "B01002_001",          # Median age
    housing_cost_burden = "B25070_010", # Housing units spending 50% or more of income on rent
    no_vehicle = "B08201_002",          # Households with no vehicle available
    black_population = "B02001_003",    # Black or African American alone population
    median_rent = "B25058_001"),        # Median contract rent
  summary_var = "B02001_001",           # Total population (for calculating proportions)
  output = "wide", geometry = FALSE)

Dimensionality in Spatial Models

Model development

Dimensionality in Spatial Models

Model development

Response vector structure (\(\boldsymbol{y}\)):

\[ \begin{align} \boldsymbol{y} &= \begin{bmatrix} y_{1} \\ y_{2} \\ \vdots \\ y_{n} \end{bmatrix} \end{align} \]

• Each element, \(y_i\), represents the observed response at a neighborhood’s location \(i\)

• These are ordered by adjacency relationships to preserve the geographical context

• Also, review of distributions, spatial autocorrelation (i.e., \(Cov(y_i, y_j)\)), and decomposition

Dimensionality in Spatial Models

Model development

Design matrix of explanatory variables structure (\(\boldsymbol{X}\)):

\[ \boldsymbol{X} = \begin{bmatrix} 1 & x_{1, 1} & \ldots & x_{1, p} \\ 1 & x_{2, 1} & \ldots & x_{2, p} \\ \vdots & \vdots & \ddots & \vdots \\ 1 & x_{n, 1} & \ldots & x_{n, p} \\ \end{bmatrix} \]

• First column is the intercept term

• Subsequent columns represent \(p\) explanatory variables

• Each row corresponds to a specific neighborhood’s covariates

Dimensionality in Spatial Models

Sample design matrix of explanatory variables

\[ \boldsymbol{X} = \begin{bmatrix} 1 & 65,000 & 0.62 & 3,200 \\ 1 & 28,000 & 0.32 & 5,100 \\ \vdots & \vdots & \vdots & \vdots \\ 1 & 127,000 & 0.75 & 6,840 \\ \end{bmatrix} \]

• Column 1 is the expected value of \(\boldsymbol{y}\) when all other predictors are zero

• Variable 1 (column 2) as median income

• Variable 2 (column 3) as the proportion of residents with a high school diploma

• Variable 3 (column 4) as population density (residents/sq. mi)

Information and spatial segregation

Model selection

There are multiple models for consideration:

Overview

• Project background and model development (Nathan, Howard University, faculty)

• Case analysis: Health (Bayowa, Howard University, M.S. Data Science)

• Dashboard: Race and ethnicity (Jibek, Howard University, Junior, B.S. Computer Science)

• Political analysis (Nathan, on behalf of our Morehouse team)

Hypertension

Hypertension, also known as high blood pressure, is a condition in which the force of blood pushing against the walls of the arteries is consistently too high.

The condition is a compounding health concern in the United States.

The prevalence of high blood pressure fluctuations over time:

• Between 1999–2000, high blood pressure was highest at 47.9%
• It reached its lowest points between 2009-2010 and 2013-2014 at 43%
• As of 2017-2020, high blood pressure had a national average of around 48%

Hypertension rate in the US

Time Trend of Hypertension Mortality Rates Over Time in the US

Comparative rates in the DMV

Bar chart of Hypertension Morbidity Rates in Proximal States

CRE and hypertension morbidity

While the Community Resilience Estimates (CRE) do not directly measure hypertension, there are several indirect connections between hypertension and community resilience:

• Health Insurance: One of the CRE risk factors is lack of health insurance. Individuals without health insurance are less likely to receive regular blood pressure screenings and treatment for hypertension.

• Socioeconomic Factors: The CRE includes factors like poverty and employment, which are known to influence hypertension rates.

• Education: Limited education is a CRE risk factor. Lower educational attainment is associated with higher rates of hypertension.

• Age: The CRE considers households with individuals aged 65 or older as a risk factor. Hypertension increases with age, making older populations more vulnerable to its effects.

CRE and hypertension morbidity for DC

Racial Differences and Hypertension Morbidity for DC

Hypertension and CRE

Political analysis

Examining the impact of broader political shifts on neighborhood measures.

• Project title: Examining Polling Location Changes After The Shelby County Decision: How a Lack of Federal Oversight Impacts Poll Accessibility in Black and Brown Communities

• Abstract: Since the Supreme Court’s Shelby Decision in 2013, states are no longer required to have polling station changes or closures federally reviewed. Given that over 1600 polling locations have been closed or changed since 2013, we ask what factors contribute to these polling location changes and closures? We examine the driving forces behind these changes, and use Census data to determine what implications these polling location changes may have on accessibility in communities of color.